We have made an energy evaluation for the rearrangement of martensite variants (RMV) under a magnetic field in four types of ferromagnetic shape memory alloys: an Fe-31.2at.%Pd with so-called fct martensite, a Ni₂MnGa with the 10M martensite, a Ni_2.02Mn_1.09Ga_0.89 with the 14M one and a Ni_2.14Mn_0.92Ga_0.94 with 2M one. From magnetic field-induced strain measurements, magnetization measurements and in-situ optical microscope observations, we found that the RMV by a magnetic field occurs at any temperature for the Fe-31.2Pd and the 10M martensite, it occurs in a limited temperature range for the 14M martensite and does not occur at any temperature for the 2M martensite. The reason of such different behavior is quantitatively explained by evaluating two shear stresses: the magnetic shear stress acting across a twinning plane τ_mag, and the stress required for the twinning plane movement τ_req. The value of τ_mag is evaluated from the magnetocrystalline anisotropy constant and the twinning shear, where the former is obtained from magnetization measurements along the easy and hard axes and the latter from the lattice parameters. On the other hand, the value of τ_req is evaluated from tensile tests or compressive tests. By comparing the value of τ_mag and τ_req thus evaluated, we have confirmed that the following condition is universal regardless of temperature, field orientation and structure of the martensite phase: the value of τ_mag is larger than τ_req when the RMV occurs by magnetic field and vice versa.

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